{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:03Z","timestamp":1753894383541,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,1,6]],"date-time":"2022-01-06T00:00:00Z","timestamp":1641427200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We show that the normal form of the Taylor expansion of a $\\lambda$-term is\nisomorphic to its B\\\"ohm tree, improving Ehrhard and Regnier's original proof\nalong three independent directions. First, we simplify the final step of the\nproof by following the left reduction strategy directly in the resource\ncalculus, avoiding to introduce an abstract machine ad hoc. We also introduce a\ngroupoid of permutations of copies of arguments in a rigid variant of the\nresource calculus, and relate the coefficients of Taylor expansion with this\nstructure, while Ehrhard and Regnier worked with groups of permutations of\noccurrences of variables. Finally, we extend all the results to a\nnondeterministic setting: by contrast with previous attempts, we show that the\nuniformity property that was crucial in Ehrhard and Regnier's approach can be\npreserved in this setting.<\/jats:p>","DOI":"10.46298\/lmcs-18(1:1)2022","type":"journal-article","created":{"date-parts":[[2022,1,7]],"date-time":"2022-01-07T08:35:56Z","timestamp":1641544556000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Taylor expansion of $\\lambda$-terms and the groupoid structure of their rigid approximants"],"prefix":"10.46298","volume":"Volume 18, Issue 1","author":[{"given":"Federico","family":"Olimpieri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lionel Vaux","family":"Auclair","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,1,6]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/8916\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/8916\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:18:00Z","timestamp":1687292280000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/6701"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,6]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(1:1)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2008.02665v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2008.02665v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2008.02665","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2008.02665","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2022,1,6]]},"article-number":"6701"}}